A survey and benchmark of high-dimensional Bayesian optimization of discrete sequences (2406.04739v2)

Abstract: Optimizing discrete black-box functions is key in several domains, e.g. protein engineering and drug design. Due to the lack of gradient information and the need for sample efficiency, Bayesian optimization is an ideal candidate for these tasks. Several methods for high-dimensional continuous and categorical Bayesian optimization have been proposed recently. However, our survey of the field reveals highly heterogeneous experimental set-ups across methods and technical barriers for the replicability and application of published algorithms to real-world tasks. To address these issues, we develop a unified framework to test a vast array of high-dimensional Bayesian optimization methods and a collection of standardized black-box functions representing real-world application domains in chemistry and biology. These two components of the benchmark are each supported by flexible, scalable, and easily extendable software libraries (poli and poli-baselines), allowing practitioners to readily incorporate new optimization objectives or discrete optimizers. Project website: https://machinelearninglifescience.github.io/hdbo_benchmark

• The paper introduces a comprehensive taxonomy and survey of high-dimensional Bayesian optimization methods for discrete sequences, clarifying similarities and differences among techniques.
• It critiques inconsistent experimental setups in current research and proposes a unified benchmarking framework using standardized libraries for reproducible evaluations.
• Benchmark results reveal that embedding-based strategies, especially latent-variable models, outperform direct discrete optimization in real-world applications.

High-Dimensional Bayesian Optimization of Discrete Sequences: A Survey and Benchmark Analysis

Overview

The paper "A survey and benchmark of high-dimensional Bayesian optimization of discrete sequences" by Miguel González-Duque et al. provides an exhaustive review of Bayesian Optimization (BO) methodologies applied to high-dimensional discrete sequence spaces. The paper highlights the application challenges and inconsistencies in experimental setups and suggests a unified framework for benchmarking BO methods. This essay explores these contributions with a focus on discrete sequence optimization problems, especially in domains such as chemistry and biology.

Background and Context

BO is recognized for efficiency in optimizing black-box functions where evaluating the function is computationally expensive. The methodology hinges on surrogate models, often Gaussian Processes (GPs), to predict the function's behavior and acquisition functions to guide the selection of subsequent points for evaluation. High-dimensional spaces, particularly those involving discrete sequences, pose unique challenges due to poor scalability with dimensionality and dataset size.

Contributions

1. Taxonomy and Survey:

   The paper classifies the myriad approaches in high-dimensional BO into a nuanced taxonomy. This taxonomy is designed to clarify the similarities and differences across various methods:

   1. Variable Selection: Techniques like Hierarchical Diagonal Sampling (HDS) and Sequential Optimization of Locally Important Directions (SOLID) address high-dimensional spaces by focusing on subsets of highly relevant variables.
   2. Additive Models: These methods, such as Add-GP-UCB, decompose the objective function into sums of lower-dimensional functions to ease the curse of dimensionality.
   3. Trust Regions: Approaches like TRIKE and TuRBO restrict optimization to local regions that are dynamically adjusted based on observed performance.
   4. Linear Embeddings: Methods like REMBO employ linear transformations to project the high-dimensional space into a lower-dimensional latent space for optimization.
   5. Non-linear Embeddings: Techniques such as latent space optimization (LSBO) leverage non-linear embeddings learned from deep generative models to optimize complex discrete spaces.
   6. Gradient Information: Here, gradients are either assumed available from the surrogate or are predicted to guide the optimization process.
   7. Structured Spaces: Approaches like GaBO directly tackle structured spaces like Riemannian manifolds or mixed-variable spaces.

2. Addressing Experimental Inconsistency: The paper criticizes existing methodologies for their heterogeneity in experimental setups. Initialization strategies and evaluation budgets vary widely, complicating direct comparisons. To mitigate this, the paper proposes a standardized framework underpinned by poli and poli-baselines software libraries. This ensures consistent initialization, evaluation, and logging across various optimization methods.

3. Benchmarking Framework: The proposed benchmarking framework evaluates BO methods using standardized objectives drawn from real-world applications, such as drug design and protein engineering. This includes a diverse array of black-box functions supported by flexible, scalable software libraries, designed to be easily extendable for new objectives or optimizers.

Numerical Results and Claims

The paper empirically compares several state-of-the-art high-dimensional BO methods on the Practical Molecular Optimization (PMO) benchmark. Results reveal:

• Methods relying on pre-trained latent-variable models significantly outperform methods optimizing directly in discrete sequence space.
• Vanilla BO implementations using informed priors perform competitively against more complex, specialized algorithms.
• Initialization and evaluation consistency provided by the unified framework (poli and poli-baselines) yields more reliable and reproducible benchmarking outcomes.

Implications and Future Directions

The findings suggest that embedding-based strategies, especially those using deep generative models for latent space optimization, hold significant promise for high-dimensional discrete sequence optimization. The discrepancies highlighted in experimental setups underscore the necessity for standardized benchmarking frameworks to ensure reproducibility and fair comparison across methodologies.

Theoretically, the taxonomy and empirical results open several avenues for further research: - Exploration of hybrid models that integrate linear and non-linear embeddings with other structural assumptions like trust regions might yield more robust optimization techniques. - Enhanced surrogate models leveraging gradient predictions or adaptive kernel designs could further alleviate scalability issues in large-dimensional spaces. - Expansion of the benchmark tasks to include more diverse and challenging real-world problems will provide deeper insights into the generalizability and practical utility of BO methods.

Conclusion

The paper by González-Duque et al. presents a rigorous survey and benchmark analysis of high-dimensional Bayesian Optimization for discrete sequences. The proposed classification of methods and the unified benchmarking framework address critical gaps in the current optimization literature. By offering a standardized approach, the paper not only provides valuable insights into the existing methods but also sets a foundation for future work aiming to optimize complex discrete sequence spaces more effectively. The practical implications for applications in chemistry and biology, among others, are profound, paving the way for more efficient and reliable optimization in these fields.